Method of making a brake band



May 25, 1959 .1.w. HOLDEMAN ETAL 2,887,771

METHOD OF MAKING A BRAKE BAND original Filed Jan. s, 1951 2 Sheets-Sheet1 May 26, 1,959 J.w. HOLDEMAN ET AL 2,887,771

METHOD OF MAKING BRAKE BAND original Filed Jn. s, 1951 2 sheets-sheet 2wfugenef'f'rrll 35%. la 62.4%

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METHOD OF MAKING A BRAKE BAND .lohn W. Holdeman, Detroit, and Eugene F.Farrell,

Grosse Pointe, Mich., assignors to Borg-Warner Corporation, Chicago,Ill., a corporation of Illinois 10 Claims. (Cl. 29-418) 4 The presentinvention relates to brake bands and more Patented May 26, tsss sume theshape of a true circle when it is constricted to its working position. y

The methodl disclosed herein consists of placing a substantiallycylindrcally shaped brake band, having its I5 ends joined by a bracketwelded thereto, around an exparticularly to a brake band for braking asubstantially circular drum element of an automotive vehicletransmission brake.

This application is a division of our copending application, S.N.204,193, tiled January 3, -195 1, now Patent No. 2,768,714, for BrakeBand.

The main object of the present invention is to provide a brake band,which when constricted to its working shape by the application of forceto each end thereof, assumes the shape of a substantially true circle sothat substantially every increment of length of the band engages thedrum.

Another object of the present invention is tot provide a method ofmaking a brake band, which, when constricted to its working position,assumes substantially the shape of a true circle.

The practice generally followed heretofore in making brake bands forbraking the rotatable drum elements of friction brakes has been to makethe band substantially circular. The first step generally followed hasbeen to place a strip of flexible material with its ends joined togetheraround an expansible mandrel. The mandrel, which is substantiallycircular, is then expanded in order .to impart its circular shape to theband. When the band is subsequently cut, it expands and assumes a sub-When forces are thereafter l must be applied to the ends of the band inorder to bring -them to their working position. This bending moment isgreatest at the mid-point of the band and tapers olf to 'zero at theends. Thus more bending occurs at the midpoint of the band and thisprevents its taking a circular pansible mandrel, the periphery of whichhas the proper amount of reverse distortion to properly shape the brakeband when the mandrel is expanded. The brake band, after having beenshaped by the expanded mandrel, is shot-peened on its inner diameter andfriction material is then cemented thereto. The bracket is then severedand the band is permitted to assume its free shape. The shape of thefree band is substantially the same as the shape orf the expandedmandrel, however, the diameter is somewhat larger. Whenv the band isthereafter compressed to its working shape by forces applied to thebrackets on either end thereof it assumes substantially the shape of atrue circle so that boring of the lining is unnecessary.`

' The method disclosed by the present invention pro` duces aneconomical, cold worked high strength band 4 wherein camber between theband and the friction lining is practically eliminated. When the band isexpanded by the expansible mandrel, the strength of the weld between thebracket and the ends of the band are electively tested. The presentmethod allows considerably less accuracy in the initial forming of theband before the shape in its work/ing position. When the brake lining isapplied to the inner surface of the band the distortion mentioned aboveis great enough to produce a considerable variation in brake liningthickness when the lining is .subsequently bored to provide a circularinner periphery when the band is constricted to its working position.

Because of the variationfin the thickness of the brake 1ining its lifeis shortened considerably. Since the brake band disclosed by the presentinvention is substantially circular when it is contracted to its workingposition, the

necessity of boring the brake lining after it is cemented ing a brakeband wherein the distortion of the band from a substantially circularshape, when it assumes its working position, is eliminated consists ofpreforming the band so as to give it the correct amount of reversedistor- .tion when in its free position tolthererby cause it `to asnbracket is fastened in place. Inasmuch as the apparatus necessary forproducing bands in accordance with the present invention is relativelyinexpensive and because expensive machining operations to control thesize of the band are unnecessary, the present invention provides a brakeband that is cheap to manufacture and has a long life.

The above and numerous other objects and advantages of the presentinvention will become apparent from the following detailed descriptionwhen read in conjunction with the accompanying drawings, wherein:

Fig. l is a plan view of the expansible mandrel constructed inaccordance with the principles of the present invention;

Fig. 2 is a graphic diagram showing `the location of the centers of thedilerent sections of the mandrel shown in Fig. l;

Fig. 3 is a side elevation view, shown partly in section, of 4themandrel disclosed in Fig. 1;

Fig. 4 shows an unlined band with its attached bracket forming a closedring that has been stretched over an expanded mandrel of the type shownin Fig. l;

Fig. 5 shows a band having friction material cemented on the innersurface thereof;

Fig. 6 shows a band in expanded condition after Vthe bracket has beensevered;

Fig. 7 shows the band compressed to its substantially circular workingposition; and

Figs. 8 and 9 show sketches utilized in computing the l shape of theexpansible mandrel.

' -With reference now to the drawings wherein like reference numeralsdesignate identical parts in the several views, and referring inparticular to Figs. l and 3, a noncircular expansible mandrel isindicated generally by reference numeral 10. The mandrel 10 comprisesthree individual segments 11, 12 and 13 and each of these segmentscovers an are of approximately Each of the segments 11, 12 and 13 has ashoulder '14 for seating a brake band 15 around the mandrel. The innerperiphery of each of the segments 11, 12 and 13 is cone shaped forreceiving a complementary cone shaped expanding member 16. As isobvious, when the member 16 is forced downwardly, as viewed in Fig. 3,the segments 11, 12 and 13 are forced outwardly to thereby engage andexpand the band 15 until it conforms substantially to the shape of theperiphery of the mandrel 10. i

As is apparent to those skilled in the art, a circularly shapedband doesnot contract to a true circle when forces are applied to its ends inorder to bring them together. Because of the fact that the bendingmoment is-greatest at the mid-point of the band and tapers off to zeroat the ends, more bending occurs at the mid-point of the band andprevents its taking a circular shape when its ends are forced towardsone another. In order to provide a band having a free shape that willconstrict to a circular shape when forces are applied to its ends, it isnecessary to determine the free shape of the band that will produce atrue circular shape when its ends are moved towards one another. Themathematical calculation utilized in. determining the free shape of aband that will compress to a circular shape when its ends are forcedtogether Will now be described. l

Referring to Fig. 8 a band or beam is 'shown in its com pressed positionin which its shape is a true circle. Fig. 9 shows the band in itsexpanded position. When the band occupies its compressed position itscenter is O and it has a constant radius r. In the free position of theband its center is still at point O but its radius is now r-l-u, where uis a variable. F is the force that must be applied to each end of theband to bring the band to its compressed position, and therefore thebending moment at any point P on the periphery of the band is Fx.However, from Fig. 8 it is apparent that x=r (l-l-cos 0) and thereforethe bending moment M is represented by the equation M=Fr(1+cos 6) (1')The differential equation of a curvedv beam where E is the modulus ofelasticity and I is the moment of in'- 'ertia of a section of the beam,is

EI d2u o 7,((192 +u)-M Fr 1+c0se The solution of this equation, usingthe rules for solving linear differential equations, is

The constants A and B depend only upon where the pole' or center O istaken relative to the compressed ring. Since the line OA is an axis ofsymmetry, u has the same value where :0 as where it equals 7T TTherefore FTS' lLn-E-I-l-.

and' u F1'3 s-rrfi Therefore, since u has the same value for 0:0 and and0=1r, A=0. When the band occupies its compressed position it assumes theshape of a true circle and under this condition u=0 throughout theperiphery of the-band and therefore 4 and consequently B==O. Thereforethe solution for Equation 3 above is But since F, r, E and I areconstants this equation may be written as follows This equationtherefore represents the shape of the band when it assumes its relaxedposition. Because of the fact that the band assumes substantially thesame shape as the expanded mandrel, even though the expanded band orfree band has a somewhat greater radius, this equation also representsthe shape of the expanded mandrel that is necessary to properly shapethe band, so that when it is compressed it will assume the shape of atrue circle.

By assigning appropriate values to F, r, E and I the shape of themandrel may be computed. The locus corresponding to the shape of themandrel may then be plotted on a scale several times the size of themandrel in order to produce `the required degree of accuracy and thenthe locus may be approximated by circular arcs. When the locus isapproximated by circular arcs it is apparent that the machining of themandrel is greatly facilitated. It has been found, where the mandrel hasa diameter of approximately 6 inches, that three substantially equalarcs are generally satisfactory for an angular expanse of zero to 180and because of the fact that the `curve is symmetrical, the range fromI180 to 360 can be obtained by inversion. This method of graphically'constructing the shape of the mandrel is somewhat difficult to carryout -to the required degree of accuracy and therefore it is preferableto use the following analytical method for arriving at the shape of themandrel.

The analytical method for determining the shape of the mandrel will nowbe described. First the x, y coordinates of the points on the curveformed by the periphery of the mandrel, for values of 0 equal to 0, 30,60, 90, 120, and 180 degrees are computed. These x, y coordinates may bedetermined by merely solving Equation 4 or 4a for the value of ucorresponding to the different values of 0, and then the x coordinatemay be determined from the equation x= (r-i-u) cos 0 and the ycoordinate may be determined from the equation y=(r}u) sin 0.

Thus, the x, y coordinates for each 30 degree point on the periphery ofthe mandrel are known. The next step is to determine the center of eachcircular arc of 60 degrees from 0:0 to 180 degrees. Three points on eachof these arcs have already been computed and from the principles ofanalytic geometry the equations for a circle through three points havingx, y coordinates equal respectively to (x0, y0), (x1, y1) and (x2, y2),and having a center whose coordinates are (h, k), are

,mammal-21u132 lspending to 9=0, 30 and 60 degrees, may be computed.same procedure may be used for determining the .centers of the arcsthrough the points corresponding to .0:160, 90 and 120 degrees,` andthrough the points corresponding to 120, 150 and 180 degrees. The otherhalf of the periphery of the mandrel is symmetrical and of course may bereadily computed. Having determined the coordinates for the center (h,k) for each arc, and since the coordinates (h, k) are known for onepoint on each arc, the radius of each arc may be determined from thefollowing equation f 'Ihe mandrel 10, shown in Fig. 1, as has alreadybeen described, has three segments 11, 12 and 13. Each of the segmentsis divided into two sections ,of approximately `60 degrees each, theperipheries of each section having centers corresponding respectively topoints 1-6, shown in Fig. 2. The mean radius of the mandrel (shown inFig. l) is 3.173 inches and each 30 degree `point on the peripherythereof has been computed in accordance. with the analytical methoddescribed above. Each 60 degree section of the mandrel 10 is identified-in Fig. Il by numerals l-6 and the centers of curvature of each ofthese sections are identified by the correspond- -ing numerals 1-6 inFig. 2. In each of the Figs. 1 and 2 the positive x-axis extends fromthe center of the ligure to the right along the horizontal and thepositive y-axis extends from the center of the ligure upwardly along thevertical. The coordinates (h, k) representing the centers of thedifferent sections and the radii for each ofthe sections, represented ininches, are given in the following table.

Center Section Radius From the above table it is apparent that theperiphery of the mandrel 10 is non-circular. However, each of thesections 1-6 has a circular curvature and this facilivtates themachining of the mandrel. Actually the shape of the periphery of theexpanded mandrel 10 approximates very closely, Equation 4 or 4a setforth above and for all practical purposes a brake band formed by themandrel shown in Fig. 1 has such a configuration that it will assume theshape of substantially a true circle Vwhen its ends are forced togetherto bring it into engagement with a circular brake drum. It is apparentthat `the configuration of the mandrel 10 and of the brake vband issubstantially cardioidal.

- In practicing the method of the present invention the mandrel 10 isrst contracted. The brake band 15, hav- 'ing its ends 17 and 18 joinedtogether by means of a -bracket 19 secured, such as by welding, to eachof the ends 17 and 18, and having a generally cylindrical configurationis placed in position over the mandrel 10. The expanding member 16 isthen driven downwardly to Acause the segments 11, 12 and 13 to expandand engage the band 15. The cardioidal shape of themandrel 10 is therebyimparted to the brake band 15. The next method step, which isillustrated in Fig. 5, comprises the fastening of a brake liner on theinner periphery of the band 15. The brake liner 20 consists of anysuitable vfriction inducing material and may be fastened to the `band bycement or any other suitable means.

The next method step consists of cutting the bracket 19 -so that itforms a pair of force receiving lugs y19a and ,19b. When the Ybracket 19is cut, the band `15 andliner l 20 expand to the position as showninFig. 6. The xpanded or free band 15 retains its cardioidal shapeeve'nthough its mean radius is somewhat greater than the mean radius of theexpanded mandrel 10. When forces F are directed in a straight linetowards each other against both of the force receiving lugs 19a and 19bthe brake band 15, together with the liner 20, is compressed and assumesa working shape that is substantially circular. Because of this circularworking shape of the band and liner it is unnecessary to bore the liner20 in order that it will engage a circular brake drum at all points onthe periphery of the liner. The reason that the band 15 assumes asubstantially circular shape when compressed by the forces F is thatmid-point 21 has the greatest radius of curvature and the radius ofcurvature progressively decreases towards either end 17 or 18 of theband. Since the bending moment at any point on the periphery of the bandis equal to the force F multiplied by the distance between that pointand the lline of application of the force F, it is apparent that thebending moment is greatest towards the mid-point 21 of the band andprogressively decreases towards the ends 17 and 18 of the band. Due tothe greater radius of curvature of the middle portions of the band theseportions must be bent more in order for them to approach a true circleand consequently since the bending moment is greater progressively fromthe end'of the band to the mid-point thereof, the sections of the bandhaving the greater radius of curvature are bent more, and thus theentire band is compressed to a substantially circular working position.

In the description above, of the method of making the brake band inaccordance with the present invention, the liner 20 has been describedas being secured to the band after the band itself has been expanded andshaped by the mandrel. It is to be noted, however, that the liner mayjust as well be attachedto the band before the band vshaping operation,if the liner is made of a material which will expand properly and willnot be distorted during the shaping operation. This method of practicingthe invention is particularly applicable to bi-metal bands when the twometals are more readily bonded together prior to thc `haping operationand one of the metals serves as the mer.

The mandrel 10 is disclosed in the drawings and described above ascomprising three substantially equiangular sections, however, this ismerely illustrative and we do not intend to be limited to thisconstruction. We therefore desire to point out that it is within therealm of the present invention to utilize a mandrel or arbor consistingof any number of sections, each of which may be either substantiallyequiangular or some or all of which maybe of substantially diiferentsizes.

When the arbor is expanded to shape the band the tendency is for theportions of the periphery of the band which lie over the spaces betweenadjacent sections to be straight but when these spaces are narrow thistendency is negligible. The size of the spaces between adjacentsections, whenthe arbor is expanded, is inversely proportional to thenumber of sections in the arbor and it is therefore sometimes `desirableto increase the number of sections to some number greater than three inorder .to decrease the size of the spaces. Even though the arbor iscomprised of more than three sections it has been found, if the overallshape of the arbor is the same as the overall shape of the three sectionarbor described herein, that the arbor will produce an entirelysatisfactory band. If it is desired to have the shape of the expandedmandrel more nearly approach Equation 4 or 4a it is within the realm ofthe present invention to have the periphery of the arbor conform to anynumber of cylindrical segments. It is thus apparent that the arbor canbe formed by first grinding the peripheral surface thereof to conform tothe desired number of cylindrical segments and then the arbor can be cutinto the desired number onfy sections` which may be equiangular or ofdifferent sizes.

As is' apparent from the above description, the present inventionprovides a brake band which when moved to its rworking position assumessubstantially the shape of a true circle. Therefore, the brake bandengages the brake drum at all points on its periphery, and because ofthe uniform initial contact, the torque handling capacity of this bandis higher than the capacity of a band which is substantially circular inthe free position. This is true because the additional force required tomake the conventional band conform to the drum, detracts from the forceavailable for braking.

It is contemplated that numerous changes may be made in the presentinvention without departing lfrom the spirit or scope thereof.

We claim:

l. The method of making a brake band having a working configurationapproximating a true circle comprising the steps of: placing a closedsubstantially cylindrical metal band which is exible and deformable forsubstantially all of its circumference around a non-circular expansiblemandrel having an external expanded periphery correspondingapproximately to the equation where u is the change in the radius of theband, E is the modulus of elasticity of the flexible metal strip, I isthe moment of inertia of the strip, r is the mean radius of the expandedmandrel, F is the force required to bend the band to a substantiallycircular shape after it has been expanded, and is the angle subtended bythe external periphery of the mandrel measured from the point on theperiphery having the greatest radius of curvature; expanding the mandrelto impart a configuration to the band corresponding substantially to theconfiguration of the external periphery of the expanded mandrel; andsevering the closed exible metal band at a point 180 from the pointhaving the greatest radius of curvature imparted thereto.

2. The method of making a brake band having a generally cardioidalrelaxed configuration and a working configuration approximating `a truecircle comprising the steps of z placing va substantially cylindricaliiexible metal strip, having its ends joined by a metal lug securelyfastened thereto, around a generally cardioidally shaped expansiblemandrel positioning the lug at a point diametrically opposite from apoint on the mandrel having the greatest radius of curvature; expandingthe mandrel a substantially equal amount at all points on its peripheryto impress the generally cardioidal shape of the mandrel to the strip;`securely fastening a uniform layer of friction inducing material on theinner periphery of said strip; and severing the lug between the ends ofthe strip to allow it to expand to a relaxed configuration, the portionof said severed lug on each end of said strip providing a forcereceiving lug whereby the ends of the band may be urged toward eachother whereupon the band assumes a substantially circular configuration.

3. The method of making a brake band having a non- 'circular relaxedconiiguration and a working configuration approximating a true circlecomprising the steps of: placing a substantially cylindrical flexiblemetal strip, having its ends joined by a metal lug securely fastenedthereto, around an expansible mandrel, the periphery of which comprisesa plurality of sections of such size and contour as to produce in theexpanded condition a substantially cardioidal shape when all of thesections are lying in the same transverse plane; positioning the lug ata point diametrically opposite from a point on the mandrel having thegreatest radius of curvature; expanding the mandrel a substantiallyequal amount at all points n its periphery to impress the shape of themandrel to the strip; securely fastening a uniform layer of frictioninducing material on the inner periphery of said'strip, and severing thelug between the ends of the strip t allow it to expand to a relaxedconfiguration, the portion of said severed lug on each end of said stripproviding a force receiving lug whereby the ends of the band may beurged toward each other whereupon the band assumes a substantiallycircular configuration.

4. The method of making a brake band having a noncircular relaxedconfiguration and a working configuration approximating a true circlecomprising the steps of: placing a substantially cylindrical flexiblemetal strip, having itsends joined by a metal lug securely fastenedthereto, around an expansible mandrel, the periphery of which comprisesa plurality of substantially circular sections, of such size and contouras to produce in the expanded condition a substantially cardioidal shapewhen all of .the sections are lying in the same transverse plane;positioning the lug at a point diametrically opposite from a point onthe mandrel having the greatest radius of curvature; expanding themandrel a substantially equal amount at all points on its periphery toimpress the shape of the mandrel to the strip; securely fastening auniform layer of friction inducing material on the inner periphery ofsaid strip; and severing the lug between the ends of the strip to allowit to expand to a relaxed configuration, the portion of said severed lugon each end of said strip providing a force receiving lug whereby theends of the band may be urged toward each other whereupon the bandassumes a substantially circular configuration.

5. The method of making a brake band having a noncircular relaxedconfiguration and a working configuration approximating a true circlecomprising the steps of: placing a substantially cylindrical fiexiblemetal strip, having its ends joined by a metal lug securely fastenedthereto, around an expansible mandrel comprising three sectionssubtending substantially equal angles at the center of the mandrel andof such size and contour as to produce in the expanded condition asubstantially cardioidal shape when all of the sections are lying in thesame transverse plane, the periphery of one of said sections comprisingtwo substantially equal length cylindrical portions having the sameradius of curvature and different centers, the peripheries of the othertwo sections each comprising two substantially equal length cylindricalportions, the cylindrical portions of said last-mentioned sectionsadjacent said one 'section having identical radii of curvature that areslightly smaller than the radii of curvature of said first two portionsand the other two portions of said other two sections being adjacenteach other and having identical radii of curvature still smaller thaneither of said other radii of curvature; positioning the lug at a pointon the mandrel from the point having the greatest radius of curvature;expanding the mandrel a substantially equal amount at all points on itsperiphery to impress the shape of the mandrel to the strip; securelyfastening a uniform layer of friction inducing material on the innerperiphery of said strip; and severing the lug between the ends of thestrip to allow it to expand to a relaxed configuration, the portion ofsaid severed lug on each end of said strip providing a force receivinglug whereby the ends of the band may be urged toward each otherWhereupon the band assumes a substantially circular configuration.

6. The method of making a brake band having a noncircular relaxedconfiguration and a working configuration approximating a true circlecomprising-the steps of: placing a substantially cylindrical flexiblemetal strip, having its ends joined by a metal lug securely fastenedthereto, around an expansible mandrel comprising a plurality of sectionseach of which subtends an angle at the center of the mandrel, saidsections being of such size and contour as to produce in the expandedcondition a substantially cardioidal shape when all of the sections arelying in the same transverse plane, the peripheral surface formed by allof said sections comprising a plurality of substantially cylindricalportions, the cylindrical portion at one point on the periphery of themandrel having a certain radius of curvature and the radii of curvatureof the other portions progressively decreasing towards the portion 180from said one portion; positioning the lug at a point on the mandrel 180from the point having the greatest radius of curvature; expanding themandrel a substantially equal amount at all points on its periphery toimpress the shape of the mandrel to the strip; and severing the lugbetween the ends of the strip tor allow it to expand to a relaxedconfiguration, the portion of said severed lug on each end of saidsevered strip providing a force receiving lug whereby the ends of theband may be urged toward each other whereupon the band assumes asubstantially circular configuration.

7. The method of making a brake band having a noncircular relaxedconfiguration and a working configuration approximating a true circlecomprising the steps of: placing a substantially cylindrical exiblemetal strip having a deformable uniform layer of friction yinducingmaterial on the inner periphery thereof and having its ends joined by ametal lug securely fastened thereto, around an expansible mandrel, theperiphery of which comprises a plurality of substantially circularsections of such size and contour as to produce in the expandedcondition a substantially cardioidal shape when al1 of the sections arelying in the same transverse plane and having `diierent radii ofcurvature and different centers; positioning the lug at a point on themandrel 180 from the point having the greatest radius of curvature;expanding the mandrel a substantially equal amount at all points on itsperiphery to impress the shape of the mandrel to the strip; and severingthe lug between the ends of the strip to allow it to expand to a relaxedconfiguration, the portion of said severed lug on each end of said stripproviding a force receiving lug whereby the ends of the band may beurged toward each other whereupon the band assumes a substantiallycircular configuration.

8. The method of making a brake band having a noncircular relaxedconguration and a working conguration approximating a true circlecomprising the steps of: placing a substantially cylindrical flexiblemetal strip, having its ends joined by a metal lug securely fastenedthereto, around an expansible mandrel, the periphery of which comprisesa plurality of substantially circular sections of such size and contouras to produce in the expanded condition a substantially cardioidal shapewhen all of the sections are lying in the same transverse plane;positioning the lug at a point on the mandrel 180 from the point havingthe greatest radius of curvature; expanding the mandrel a substantiallyequal amount at all points on its periphery to impress the shape of themandrel to the strip; and severing the lug between the ends of the stripto allow it to expand to a relaxed configuration, the portion 10 of saidsevered lug on each end of said strip providing a force receiving lugwhereby the ends of the band may be urged toward `each other whereuponthe band assumes a substantially circular configuration.

9. The method of making a brake band having a noncircular relaxedconguration and a working coniguration approximating a true circlecomprising the steps of: providing a substantially cylindrical metalstrip having its ends joined by a relatively short metal lug secured tosaid ends; providing an expansible mandrel comprising a plurality ofarcuate sections of such size and contour as to produce in the expandedcondition a substantially cardioidal shape when all of the sections arelying in the same transverse plane and the expanded periphery isslightly greater than the periphery of the substantially cylindricalband and of the circular periphery desired in closed band; placing saidband around said mandrel with said lug spaced from the point of greatestradius of curvature of the mandrel; expanding the mandrel to impart tothe band a cardioidal conguration corresponding to that of the expandedmandrel; and severing the lug at its center for thereby providing forcereceiving lugs on the ends of said band.

l0. The method of making a brake band having a non-circular relaxedconiiguration and a working configuration approximating a true circlecomprising the steps of providing a substantially cylindrical flexiblemetal band having its ends joined by a metal lug securely fastenedthereto; providing an expansible mandrel of a substantially cardioidalshape corresponding approximately to the equation where u is the changein the radius of the band, E is the modulus of elasticity of the exiblemetal strip, I is the moment of inertia of the strip, r is the meansradius of the expanded mandrel, F is the force required to bend the bandto a substantially circular shape after it has been expanded, and 0 isthe angle subtended by the external periphery of the mandrel measuredfrom the point on the periphery having the greatest radius of curvature;placing said band on said mandrel with said lug positioned at a point180 from the point of greatest radius of curvature of the mandrel;expanding the mandrel to impart to the band a cardioidal configurationcorresponding to that of the expanded mandrel; and severing the lugthrough the center thereof to provide force receiving lugs on the end ofsaid band.

References Cited in the le of this patent UNITED STATES PATENTS1,732,630 Bennet s oct 22, 1929

